Thursday, January 07, 2010

Q: Write down the digits from 2 to 7, in order. Add two mathematical symbols to get an expression equaling 2010. What symbols are these?

Yippee! A math puzzle for 2010. The most obvious question is, do you need to get fancy with symbols beyond the standard operations of multiplication, division, addition and subtraction? For example, do you need to use a decimal point, factorials, exponentiation, square roots, etc.? Would Will be so diabolical or would he start us off easy in 2010?

I will say, using just the standard four operations between the digits, you can get 160 different results (4 x 4 x C(5,2) = 160). Of these results, 69 are positive integers. Once you have solved the puzzle for 2010, have fun seeing if you can create any of these results: 1, 623, 1102, 1103, 2291, 4572 or 4573. Also, what's the largest number you can create with just the standard operations?

Edit: The largest number you can form is 2345x6x7 = 98,490. If you study that number you'll see it is 49 times the desired solution of 2010. So just divide by 7 instead of multiplying.

36 comments:

Here's my standard reminder... don't post the answer or any outright spoilers before the deadline of Thursday at 3pm ET. If you know the answer, click the link and submit it to NPR, but don't give it away here. Thank you.

Blaine, I think you may be right though your answer is slightly esoteric :) For everyone else, I may not have made myself clear. So at the risk of repeating myself...

The rules for my puzzle are exactly the same as the rules for Will’s on-air puzzle: use all of the digits in the order given – 2 3 4 5 5 6 7 – insert two mathematical operators and come up with an expression that equals 2010. The only difference between mine and Will’s is that there are two 5s instead of one.

I wrote a program for this in VBA for Excel.Is that cheating? For me, that's usually the fun I get out of solving many puzzles. I did spend about 20 minutes off and on guessing, then 20 minutes writing the program to solve.Thanks, Blaine for a great blog.A clue for the correct answer? Call on Blaine for the info.

Tinyc Tim, some of your answers require rounding but we got some of the same answers. I used a spreadsheet and came up with 69 positive integers. As Lorenzo noted, you can get a few more answers if you use a negation sign in front, like -23+4567

Ben, I think your definition of () as a single symbol might be considered too "creative", but that does indeed come out to 2010. Is that what you submitted?

Thanks for playing Ken's Puzzle #2: A Night at the Opera. Other Ben proved to be the primo uomo of solvers. His response was very quick ... prompter than I expected. This almost caused him to be a self-promoter.

The new week puzzle is up. Think of a familiar 10-letter hyphenated word that uses all seven letters of the alphabet from "F" to "L" plus three other letters of your choosing. What word is it? It's a word everyone knows, and it's in some dictionaries. Will has got to be kidding with this one. It wasn't in ANY dictionary I own.

Tinyc Tim,Check the other thread for more clues on the 1/10/2010 puzzle. There are (7+3)!/3! ways (604,800 ways) to arrange 7 distinct items and 3 similar items. So if you want to brute force all the arrangements, you still have a few more combinations to generate and then review.